Space of modular forms of level 150, weight 5, and Character 150.f

• Label: 150.5.f
• Level: $150$
• Weight: $5$
• Character orbit: 150.f
• Rep. character: $\chi_{150}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $150$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	150.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(150\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(150, [\chi])\).

	Total	New	Old
Modular forms	264	24	240
Cusp forms	216	24	192
Eisenstein series	48	0	48

Trace form

\( 24 q - 40 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
150.5.f.a	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None					30.5.f.b	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(-68\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\beta _{2})q^{2}+3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
150.5.f.b	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None		✓			150.5.f.b	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(-48\)	$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2\beta _{2})q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+\cdots\)
150.5.f.c	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None		✓			150.5.f.c	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(192\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\beta _{2})q^{2}-3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
150.5.f.d	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None		✓			150.5.f.c	$2$	$0$	\(8\)	\(0\)	\(0\)	\(-192\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2\beta _{2})q^{2}+3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
150.5.f.e	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None					30.5.f.a	$2$	$0$	\(8\)	\(0\)	\(0\)	\(28\)	$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2+2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{6}+\cdots\)
150.5.f.f	$150$	$5$	150.f	5.c	$4$	$4$	$2$	$15.505$	\(\Q(i, \sqrt{6})\)	None		✓			150.5.f.b	$2$	$0$	\(8\)	\(0\)	\(0\)	\(48\)	$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2+2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)